STEPPING UP FOR SUCCESS ON THE MATH SOL:
TAKING THE NEXT STEPS TOWARD AUTHENTIC ASSESSMENT
Note to our PLN network:
This booklet is a WORKBOOK designed to be an interactive document. An electronic copy
is available at flexiblecreativity.com. Thank you…the management!
“We can, whenever and wherever we choose, successfully teach all
children whose schooling is of interest to us. We already know
more than we need to do that. Whether or not we do it must finally
depend on how we feel about the fact that we haven’t so far.”
~Ron Edmonds
PREPARED FOR THE COLLABORATIVE LEARNING NETWORK OF THE
VIRGINIA SCHOOL-UNIVERSITY PARTNERSHIP
BY DAN MULLIGAN, FLEXIBLECREATIVITY.COM
OCTOBER 2014
TABLE OF CONTENTS
THE IMPORTANCE OF ‘I’
3
MEASURING YOUR PRACTICE
5
LEARNING STRUCTURES TO CHECK FOR/BUILD BACKGROUND KNOWLEDGE
7
PREPARING FOR COMPUTER ADAPTIVE ASSESSMENT
10
AUTHENTIC ASSESSMENT: SAMPLE SOL SCRIMMAGE
25
ALIGNMENT OF DOK AND RIGOR/RELEVANCE FRAMEWORK
29
FAMILIAR WORDS
33
RIGOR: PRODUCTS, ROLES, AND STRUCTURES
35
DOK/QUADRANTS: VERBS AND PRODUCTS
36
DOK/QUADRANTS: STRUCTURES
37
PUTTING IT TOGETHER: TYPE OF THINKING + DEPTH OF THINKING
41
THE SECOND QUESTION
46
AUTHENTIC ASSESSMENT: A DEEPER UNDERSTANDING
48
2
THE IMPORTANCE OF ‘I’ STATEMENTS AND EXPERIENCES
The research study identifies “Six Principles for Building an Indirect Approach” to
building background knowledge.
1. The first principle is that students store background knowledge in “bimodal
packets” and that these packets or “memory records” are based on eight
“propositions” related to an “I” event, one in which the student is directly involved:
 what “I” did,
 how I felt,
 what I did to something,
 where I did something,
 what I did for or gave to someone,
 what happened to me during the event,
 what someone else did for me, and
 how I felt at the end of the event.
The specific details of the experience are “translated” into generalizations that
the student then has available in his/her fluid intelligence. Further, the bimodal
nature of the memory packet allows the student to connect the linguistic part of
the memory [words] to nonlinguistic interpretation such as visual or mental
images, sounds, smells, sensations of touch, and even emotions.
2. The second principle is that helping students store their experiences in
permanent memory can be enhanced. Students need minimally four exposures
to new content, no more than two days apart, but the four exposures cannot be
mere repetition; the four exposures must provide a variety of elaborations of the
new content without requiring students to access another knowledge set.
3. The third principle acknowledges that while the target for instruction must be
content-specific information, a student’s background knowledge outside the
target content area can be a valuable tool as the student personalizes the new
information.
4. The fourth principle emphasizes the need to increase opportunities for students
to build academic knowledge through multiple exposures to the surface-level or
basic terminology or concepts for a content area; teachers cannot build “more”
background knowledge until their students have acquired the basic information.
5. The fifth principle promotes building background knowledge through vocabulary
acquisition. Words are the labels students store in their memory packets, not just
for single objects but rather for groups or families of objects. For example, when
a child hears the word “store,” that child will pull all background knowledge that
3
connects “store” to grocery store, convenience store, department store, etc., only
if the student has a memory packet that allows him/her to explore different kinds
of stores.
6. The sixth principle discusses using virtual experiences to enhance background
knowledge. A student’s ability to read is obviously important for virtual
experiences; however, equally important is the use of spoken language for virtual
experience. Conversation, then, is an important instructional tool that should be
used in the required multiple exposures for building students’ background
information.
SOMETHING SOUNDS FAMILIAR HERE…
Additionally, students need to be provided sustained, uninterrupted silent reading time,
allowed to identify topics of interest to them, and required to write about what they
read. Through “academic” notebooks (aka, interactive notebooks), students reveal
thoughts, ideas, reservations, etc. The connection between what is read and what is
written helps establish and support the acquisition of background knowledge. While
“expressive journals” are important after reading literature, academic notebooks may
ask students to respond to questions like “How would you use this information?” or
“What do you find interesting about this information?” These notebooks may ask
students to represent what they read with a graphic or a picture. Having students share
their notebooks with others is another way to support the building process for
background information through conversation and a reinforcement of the students’
understanding or reaction.
FOCUS ON VOCABULARY
Research supports the positive results of direct vocabulary instruction, and this
instruction typically involves ten to twelve words a week from high-frequency word lists
that are grade and content-appropriate. However, problems exist, in part, because
most “high frequency” word lists do not address the difficulty, appropriateness, or
relevance of a word to a concept.
The eight characteristics of effective vocabulary instruction begins with the most
important: Dictionary definitions should not be the first exposure for students to new
words. Two of the other characteristics are, perhaps, more obvious:
Students must have multiple exposures to words and word meanings, and teaching
word parts supports student learning. Another important characteristic is that students
are provided the opportunity to discuss the words they are learning. Research confirms
that content-specific terms are most helpful in building academic vocabulary and
credits the standards movement with helping shape national recommendations for
these terms
4
6
7
8
9
A CHILD CENTERED APPROACH TO THE SOL: PREPARING FOR COMPUTER ADAPTIVE TEST (CAT)
One of the primary factors in improving student achievement is the
degree to which students have been sufficiently engaged in the
knowledge, skills, processes, and vocabulary they will be held
accountable to master.
KINDERGARTEN
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes- At a Glance
Target for Understanding: Whole Number Operations
K.6
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a. Combine two sets with known quantities in each set,
and count the combined set using up to 10 concrete
objects, to determine the sum, where the sum is not
greater than 10
b. Given a set of 10 or fewer concrete objects, remove,
take away, or separate part of the set and determine the
result
10
GRADE 1
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes – At a Glance
Target for Understanding: Whole Number Operations
1.4
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a. Select a reasonable order of magnitude for a given set
from three given quantities: a one-digit numeral, a twodigit numeral, and a three-digit numeral (e.g., 5, 50, and
500 jelly beans in jars) in a familiar problem situation
b. Given a familiar problem situation involving magnitude,
explain why a particular estimate was chosen as the
most reasonable from three given quantities: a onedigit numeral, a two-digit numeral, and a three-digit
numeral
1.5
a. Identify + as a symbol for addition, − as a symbol for
subtraction, and = as a symbol for equality
b. Recall and state orally the basic addition facts for sums
with two addends to 18 or less and the corresponding
subtraction facts
c. Recall and write the basic addition facts for sums to 18
or less and the corresponding subtraction facts, when
addition or subtraction problems are presented in
either horizontal or vertical written format
1.6
a. Interpret and solve oral or written story and picture
problems involving one-step solutions, using basic
addition and subtraction facts (sums to 18 or less and
the corresponding subtraction facts)
b. Identify a correct number sentence to solve an oral or
written story and picture problem, selecting from
among basic addition and subtraction facts
11
GRADE 2
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes – At a Glance
Target for Understanding: Number Relationships and Operations
2.5
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a. Recall and write the basic addition facts for sums to 20
or less and the corresponding subtraction facts, when
addition or subtraction problems are presented in
either horizontal or vertical written format
2.6
a. Regroup 10 ones for 1 ten, using Base-10 models, when
finding the sum of two whole numbers whose sum is 99
or less
b. Estimate the sum of two whole numbers whose sum is
99 or less and recognize whether the estimation is
reasonable
c. Find the sum of two whole numbers whose sum is 99 or
less, using Base-10 models, such as Base-10 blocks and
bundles of tens
d. Solve problems presented vertically or horizontally that
require finding the sum of two whole numbers whose
sum is 99 or less, using paper and pencil
e. Solve problems, using mental computation strategies,
involving addition of two whole numbers whose sum is
99 or less
2.7
a. Regroup 1 ten for 10 ones, using Base-10 models, such
as Base-10 blocks and bundles of tens
b. Estimate the difference of two whole numbers each 99
or less and recognize whether the estimation is
reasonable
c. Find the difference of two whole numbers each 99 or
less, using Base-10 models, such as Base-10 blocks and
bundles of tens
d. Solve problems presented vertically or horizontally that
require finding the difference between two whole
numbers each 99 or less, using paper and pencil
e. Solve problems, using mental computation strategies,
involving subtraction of two whole numbers each 99 or
less
continued on next page
12
GRADE 2
Name: ______________________________
page 2 of 2
2.8
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a. Identify the appropriate data and the operation needed
to solve an addition or subtraction problem where the
data are presented in a simple table, picture graph, or
bar graph
b. Solve addition and subtraction problems requiring a
one- or two-step solution, using data from simple
tables, picture graphs, bar graphs, and everyday life
situations
c. Create a one- or two-step addition or subtraction
problem using data from simple tables, picture graphs,
and bar graphs whose sum is 99 or less
2.9
a. Determine the missing number in a number sentence
(e.g., 3 + __ = 5 or __+ 2 = 5; 5 – __ = 3 or 5 – 2 = __)
b. Write the related facts for a given addition or
subtraction fact (e.g., given 3 + 4 = 7, write 7 – 4 = 3 and
7 – 3 = 4)
13
GRADE 3
Name: _________________________
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes – At a Glance
Target for Understanding: Computation and Fraction Operations
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a. Determine whether an estimate or an exact answer is an
appropriate solution for practical addition and
subtraction problem situations involving single-step and
multistep problems
b. Determine whether to add or subtract in practical
problem situations
c. Estimate the sum or difference of two whole numbers,
each 9,999 or less when an exact answer is not required
d. Add or subtract two whole numbers, each 9,999 or less
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e. Solve practical problems involving the sum of two whole
numbers, each 9,999 or less, with or without regrouping,
using calculators, paper and pencil, or mental
computation in practical problem situations
f. Solve practical problems involving the difference of two
whole numbers, each 9,999 or less, with or without
regrouping, using calculators, paper and pencil, or mental
computation in practical problem situations
g. Solve single-step and multistep problems involving the
sum or difference of two whole numbers, each 9,999 or
less, with or without regrouping
3.5
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a. Recall and state the multiplication and division facts
through the twelves table
b. Recall and write the multiplication and division facts
through the twelves table
3.6
a. Model multiplication, using area, set, and number line
models
b. Model division, using area, set, and number line models
c. Solve multiplication problems, using the multiplication
algorithm, where one factor is 99 or less and the second
factor is 5 or less
d. Create and solve word problems involving multiplication,
where one factor is 99 or less and the second factor is 5
or less
continued on next page
14
GRADE 3
Name: _________________________
page 2 of 2
3.7
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a. Demonstrate a fractional part of a whole, using
1. region/area models (e.g., pie pieces, pattern blocks,
geoboards, drawings)
2. set models (e.g., chips, counters, cubes, drawings)
3. length/measurement models (e.g., nonstandard units
such as rods, connecting cubes, and drawings)
b. Name and write fractions and mixed numbers
represented by drawings or concrete materials
c. Represent a given fraction or mixed number, using
concrete materials, pictures, and symbols. For example,
write the symbol for one-fourth and represent it with
concrete materials and/or pictures
d. Add and subtract with proper fractions having like
denominators of 12 or less, using concrete materials and
pictorial models representing area/regions (circles,
squares, and rectangles), length/measurements (fraction
bars and strips), and sets (counters)
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GRADE 4
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes – At a Glance
Target for Understanding: Whole Number, Fraction, and Decimal Operations, & Estimation
4.4
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a. Estimate whole number sums, differences,
products, and quotients.
b. Refine estimates by adjusting the final amount,
using terms such as closer to, between, and a little
more than.
c. Determine the sum or difference of two whole
numbers, each 999,999 or less, in vertical and
horizontal form with or without regrouping, using
paper and pencil, and using a calculator.
d. Estimate and find the products of two whole
numbers when one factor has two digits or fewer
and the other factor has three digits or fewer, using
paper and pencil and calculators.
e. Estimate and find the quotient of two whole
numbers, given a one-digit divisor and a two- or
three-digit dividend.
f. Solve single-step and multistep problems using
whole number operations.
g. Verify the reasonableness of sums, differences,
products, and quotients of whole numbers using
estimation.
continued on next page
16
GRADE 4
Name: _________________________
page 2 of 2
4.5
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a. Find common multiples and common factors of
numbers.
b. Determine the least common multiple and greatest
common factor of numbers.
c. Use least common multiple and/or greatest
common factor to find a common denominator for
fractions.
d. Add and subtract with fractions having like
denominators whose denominators are limited to 2, 3,
4, 5, 6, 8, 10, and 12, and simplify the resulting
fraction using common multiples and factors.
e. Add and subtract with fractions having unlike
denominators whose denominators are limited to 2,
3, 4, 5, 6, 8, 10, and 12, and simplify the resulting
fraction using common multiples and factors.
f. Solve problems that involve adding and subtracting
with fractions having like and unlike denominators
whose denominators are limited to 2, 3, 4, 5, 6, 8,
10, and 12, and simplify the resulting fraction using
common multiples and factors.
g. Add and subtract with decimals through thousandths,
using concrete materials, pictorial representations, and
paper and pencil.
h. Solve single-step and multistep problems that
involve adding and subtracting with fractions and
decimals through thousandths.
17
GRADE 5
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes – At a Glance
Target for Understanding: Computation Operations and Estimations
5.4
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a. Select appropriate methods and tools from among
paper and pencil, estimation, mental computation, and
calculators according to the context and nature of the
computation in order to compute with whole numbers.
b. Create single-step and multistep problems involving
the operations of addition, subtraction, multiplication,
and division with and without remainders of whole
numbers, using practical situations.
c. Estimate the sum, difference, product, and quotient of
whole number computations.
a. Solve single-step and multistep problems involving
addition, subtraction, multiplication, and division with
and without remainders of whole numbers, using paper
and pencil, mental computation, and calculators in
which
1. sums, differences, and products will not exceed five
digits;
2. multipliers will not exceed two digits;
3. divisors will not exceed two digits; or
d. dividends will not exceed four digits.
e. Use two or more operational steps to solve a
multistep problem. Operations can be the same or
different.
continued on next page
18
GRADE 5
Name: _________________________
page 2 of 3
5.5
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a. Determine an appropriate method of calculation to find
the sum, difference, product, and quotient of two
numbers expressed as decimals through thousandths,
selecting from among paper and pencil, estimation,
mental computation, and calculators.
b. Estimate to find the number that is closest to the sum,
difference, and product of two numbers expressed as
decimals through thousandths.
c. Find the sum, difference, and product of two numbers
expressed as decimals through thousandths, using
paper and pencil, estimation, mental computation, and
calculators.
d. Determine the quotient, given a dividend expressed as a
decimal through thousandths and a single-digit divisor.
For example, 5.4 divided by 2 and 2.4 divided by 5.
e. Use estimation to check the reasonableness of a sum,
difference, product, and quotient.
f. Create and solve single-step and multistep
problems.
g. A multistep problem needs to incorporate two or
more operational steps (operations can be the same
or different).
5.6
a. Solve single-step and multistep practical problems
involving addition and subtraction with fractions
having like and unlike denominators.
Denominators in the problems should be limited to
1 1
12 or less (e.g., 5 + 4 ) and answers should be
expressed in simplest form.
b. Solve single-step and multistep practical problems
involving addition and subtraction with mixed
numbers having like and unlike denominators, with
and without regrouping. Denominators in the
problems should be limited to 12 or less, and
answers should be expressed in simplest form.
c. Use estimation to check the reasonableness of a sum or
difference.
continued on next page
19
GRADE 5
Name: _________________________
page 3 of 3
5.7
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a. Simplify expressions by using the order of operations in
a demonstrated step-by-step approach.
b. Find the value of numerical expressions, using the
order of operations.
c. Given an expression involving more than one
operation, describe which operation is completed
first, which is second, etc.
20
GRADE 6
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes – At a Glance
Target for Understanding: Applications of Operations with Rational Numbers
6.6
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a. Multiply and divide with fractions and mixed
numbers. Answers are expressed in simplest form.
b. Solve single-step and multistep practical problems that
involve addition and subtraction with fractions and
mixed numbers, with and without regrouping, that
include like and unlike denominators of 12 or less.
Answers are expressed in simplest form.
c. Solve single-step and multistep practical problems
that involve multiplication and division with
fractions and mixed numbers that include
denominators of 12 or less. Answers are expressed
in simplest form.
6.7
a. Solve single-step and multistep practical problems
involving addition, subtraction, multiplication and
division with decimals expressed to thousandths with
no more than two operations.
6.8
a. Simplify expressions by using the order of
operations in a demonstrated step-by-step
approach. The expressions should be limited to
positive values and not include braces { } or
absolute value | |.
b. Find the value of numerical expressions, using
order of operations, mental mathematics, and
appropriate tools. Exponents are limited to positive
values.
21
GRADE 7
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes- At a Glance
Target for Understanding: Application of Rational Operations and Proportional Reasoning
7.3
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a. Model addition, subtraction, multiplication and
division of integers using pictorial representations
of concrete manipulatives.
b. Add, subtract, multiply, and divide integers.
c. Simplify numerical expressions involving addition,
subtraction, multiplication and division of integers
using order of operations.
d. Solve practical problems involving addition,
subtraction, multiplication, and division with
integers.
7.4
a. Write proportions that represent equivalent
relationships between two sets.
b. Solve a proportion to find a missing term.
c. Apply proportions to convert units of measurement
between the U.S. Customary System and the metric
system. Calculators may be used.
d. Solve practical problems involving addition,
subtraction, multiplication, and division with
integers.
e. Apply proportions to solve practical problems,
including scale drawings. Scale factors shall have
denominators no greater than 12 and decimals no
less than tenths. Calculators may be used.
f. Using 10% as a benchmark, mentally compute 5%,
10%, 15%, or 20% in a practical situation such as
tips, tax and discounts.
g. Solve problems involving tips, tax, and discounts.
Limit problems to only one percent computation
per problem.
22
GRADE 8
Name: ______________________
COMPUTATION AND ESTIMATION
Essential Knowledge Skills and Processes- At a Glance
Target for Understanding: Practical Applications of Operations with Real Numbers
8.3
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a. Write a proportion given the relationship of equality
between two ratios.
b. Solve practical problems by using computation
procedures for whole numbers, integers, fractions,
percents, ratios, and proportions. Some problems may
require the application of a formula.
c. Maintain a checkbook and check registry for five or
fewer transactions.
d. Compute a discount or markup and the resulting sale
price for one discount or markup.
e. Compute the percent increase or decrease for a onestep equation found in a real life situation.
f. Compute the sales tax or tip and resulting total.
g. Substitute values for variables in given formulas. For
example, use the simple interest formula I  prt to
determine the value of any missing variable when given
specific information.
h. Compute the simple interest and new balance earned in
an investment or on a loan for a given number of years.
8.4
a. Substitute numbers for variables in algebraic
expressions and simplify the expressions by using the
order of operations. Exponents are positive and limited
to whole numbers less than 4. Square roots are limited
to perfect squares.
b. Substitute numbers for variables in algebraic
expressions and simplify the expressions by using the
order of operations. Exponents are positive and limited
to whole numbers less than 4. Square roots are limited
to perfect squares.
continued on next page
GRADE 8
Name: _________________________
page 2 of 2
8.5
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a. Identify the perfect squares from 0 to 400.
b. Identify the two consecutive whole numbers between
which the square root of a given whole number from 0 to
400 lies (e.g., 57 lies between 7 and 8 since 72 = 49 and
82 = 64).
c. Define a perfect square.
d. Find the positive or positive and negative square
roots of a given whole number from 0 to 400. (Use
the symbol
to ask for the positive root and 
when asking for the negative root.)
24
Sample SOL Scrimmage
Dan Mulligan, flexiblecreativity.com
VERSION: 1.0
Benchmark/EKS: I can multiply a fraction or a whole number by a fraction and
use a visual fraction model to represent the equation.
Read carefully and follow the directions: SHOW YOUR THINKING!
1. Alice drank 3
4
of a
1
gallon of chocolate milk.
2
2. Multiply. Write your answer in simplest
form:
How much of a whole gallon did she drink? Write
your answer in simplest form.
1
x3=
4
Answer: ______
Answer: ______
Draw lines and shade in the rectangle to
represent the fraction.
Draw lines and shade in the squares to
represent the product.
3. Create a multiplication problem of a
fraction and whole number.
4. Multiply. Write your answer in simplest
form.
5 2
x
6 3
Problem: ___________
Shade the circles to represent the
problem.
Answer: ______
Use the rectangle below to represent the
problem.
Explain your thinking.
Sample SOL Scrimmage
Dan Mulligan, flexiblecreativity.com
VERSION: 2.0
Benchmark/EKS: I can
Read carefully and follow the directions: SHOW YOUR THINKING!
The chart below tells the lengths of six different rivers from around the world. Use the
lengths to complete the activities below the chart.
Name of
river
Length in
miles
Nile
Columbia
Mekong
Danube
Volga
Amazon
4,132 miles
1,450 miles
2,705 miles
1,795 miles
3,645 miles
3,976 miles
1. Fill in the blanks so each statement
is true.
2. Which of the expressions below is
equivalent to the 4 in the Columbus
River?
The value of 7 in the Danube’s length is
ten times the value of the 7 in which river’s Place a  next to all that apply.
length? _________________
___ 400 x 10 ___ 4,000 x 10
The value of 5 in which river’s length is ten
times the value of the 5 in the Volga’s
___ 4 x 100
___ 40 x 10
length.
The value of which river’s length is ten
times the value of the same digit in the
Danube’s length.
3. Circle each length that has a 6 that
is worth ten times as much as the 6
in the Volga’s length.
___ 400 ÷ 10
___ 4,000 ÷ 10
4 Explain how you used what you know
about place value to help answer the
questions in numbers 1 – 3.
26,175 miles 9,062 miles 64,582 miles
6,419 miles
40,678 miles
26
Sample SOL Scrimmage
Dan Mulligan, flexiblecreativity.com
VERSION: 1.0
Benchmark/EKS: I can
Read carefully and follow the directions: SHOW YOUR THINKING!
2. Compare the values of each 7 in the
number 771,548. Use pictures,
numbers and words to explain.
3. Norfolk State University’s Football
Stadium has a seating capacity of
31,452.
According to the 2010 census, the
population of San Jose, CA was
approximately ten times the amount of
people that NSU’s stadium can seat. What
was the population of San Jose in 2010?
Explain your reasoning.
4. How is the digit 2 in the number 582
similar to and different from the digit 2
in the number 528?
5. Tonya was practicing her
multiplication with the following facts:
9 x 10 = 90, 13 x 10 = 130, 456 x 10 = 4,500
She noticed that every time she
multiplied by ten there was a zero at the
end of each number.
Explain to Tonya why there is a zero at
the end of a number when it is multiplied
by 10.
27
Sample SOL Scrimmage
Dan Mulligan, flexiblecreativity.com
VERSION: 2.0
Benchmark/EKS: I can
Read carefully and follow the directions: SHOW YOUR THINKING!
The chart below tells the lengths of six different rivers from around the world. Use the
lengths to complete the activities below the chart.
Name of
river
Length in
miles
Nile
Columbia
Mekong
Danube
Volga
Amazon
4,132 miles
1,450 miles
2,705 miles
1,795 miles
3,645 miles
3,976 miles
2. Fill in the blanks so each statement
is true.
2. Which of the expressions below is
equivalent to the 4 in the Columbus
River?
The value of 7 in the Danube’s length is
ten times the value of the 7 in which river’s Place a  next to all that apply.
length? _________________
___ 400 x 10 ___ 4,000 x 10
The value of 5 in which river’s length is ten
times the value of the 5 in the Volga’s
length.
The value of which river’s length is ten
times the value of the same digit in the
Danube’s length.
4. Circle each length that has a 6 that
is worth ten times as much as the 6
in the Volga’s length.
___ 4 x 100
___ 40 x 10
___ 400 ÷ 10
___ 4,000 ÷ 10
4 Explain how you used what you know
about place value to help answer the
questions in numbers 1 – 3.
26,175 miles 9,062 miles 64,582 miles
6,419 miles
40,678 miles
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Rigor/Relevance Framework
The framework is a tool established by the International Center for Leadership in
Education to assist educators in examining curriculum, instruction, and assessment.
The Rigor/Relevance Framework is based on two dimensions of higher standards and
authentic student engagement.
1. Higher Standards – First, there is the knowledge continuum
that describes the increasingly complex ways in which we
think. The Knowledge Taxonomy is based on the six levels
of Bloom’s Revised Taxonomy.
Assimilatio
n of
Knowledge
Acquisition
(RIGOR)
of
Knowledge
The low end of this continuum involves acquiring knowledge and being able to recall or locate that
knowledge in a simple manner. The high end of the Knowledge Taxonomy is evident when the
learners takes several pieces of information and combine them in both logical and creative ways.
Students can solve multistep problems and create unique work and solutions.
Remembering
Understanding
Applying
Analyzing
2. Application Model – The second continuum describes
putting knowledge to use.. The five levels of this action
continuum are:
a)
b)
c)
d)
e)
Knowledge in one discipline
Apply in one discipline
Apply across disciplines
Apply to real-world predictable situations
Apply to real-world unpredictable situations
Thinking
Continuum
Evaluating
Creating
Action Continuum
Acquisition
of
Knowledge
Application
of
Knowledge
(RELEVANCE)
The Application Model describes putting knowledge to use. While low end is knowledge acquired for
its own sake, the high end signifies action – use of the knowledge to solve complex real-world
problems and to create projects, designs, and other works for use in real-world situations.
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Rigor –
Rigor refers to academic rigor — learning in which students demonstrate a thorough, in-depth
mastery of challenging tasks to develop cognitive skills through reflective thought, analysis,
problem-solving, evaluation, or creativity. (think Bloom’s)
Rigor should be thought of as how often we require our students to solve complex problems,
apply what they have learned, and critically analyze the results. The focus of rigor should be
on helping the students develop a deeper understanding of the subject matter that goes
beyond memorizing, reciting and restating. The development of critical thinking skills is
paramount to "rigor". Teachers shouldn't take pride in the fact that a student has to do two
hours of homework per night and study three days for tests in order to pass their class. In
fact, absent the true "rigor" of higher-order thinking skills, this could be considered poor
teaching practice.
Relevance –
Relevance refers to learning in which students apply core knowledge, concepts, or skills to
solve real-world problems. Relevant learning is interdisciplinary and contextual. Student work
can range from routine to complex at any school grade and in any subject. Relevant learning is
created, for example, through authentic problems or tasks, simulation, service learning,
connecting concepts to current issues, and teaching others. (think student interest)
All educators have heard the phrase, "Why do I have to learn this? I'll never use it again." If
students have to ask this question, then "relevance" is missing in the classroom. Relevance
refers to how the subject matter relates to the student's interests and needs. Real relevance
cannot be developed unless students are allowed to utilize their learning in real-life situations
and contexts. When this is considered, it is easy to see how "rigor" and "relevance" begin to
overlap. When students are allowed to apply their learning to real-world situations (relevance),
they are required to use higher-order thinking skills (rigor). Therefore, true rigor is very
difficult to attain in the absence of relevance, and vice versa.
Relationships –
Relationships involve teaching a rigorous and relevant curriculum while understanding each
student’s needs and barriers to learning (think differentiation) Core Values – Myself, as your
teacher, taking the time to understand when you don’t.
Although "rigor" and "relevance" are keys to meaningful student learning, this learning cannot
occur in the absence of "relationships" in the school. Kids cannot learn if their social and
emotional needs have not been satisfied. We can have the most rigorous and relevant classrooms
in the country, but if our kids' affective needs are not being met, we will not be successful. In a
school focused on relationships, there is a caring, student-centered environment where students
feel a sense of connection to their school. Many schools have realized the importance of this
variable, and have tried to account for it through the development of the "school within a
school" concept. In this structure, interdisciplinary teams are developed and groups of students
are assigned to each team. Others have adopted an "advisory" structure, where each teacher is
assigned a small group of students.
Results – Results refer to accountability to each student to do all in our power to assist them reach
their true potential. The focus on the results of student learning using multiple indicators is nonnegotiable, so our teachers can adjust their practices and schools can offer personalized support to
students. (think college and career ready)
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Rigor/Relevance Framework
Creating: “putting together”



Use old ideas to create new ones
Relate knowledge from several areas
Reorganize parts to create new original
things, ideas, concepts



Evaluating: “judge the outcome”



Compare and discriminate between
ideas
Assess values of theories,
presentations
Make choices on reasoned arguments



See patterns/relationships
Recognize hidden parts
Take ideas/learning apart
Find unique characteristics

Use the information
Use methods, concepts, theories in
new situations



Understand information
Translate knowledge into new context
Grasp meaning of materials learned,
communicate learnings, and interpret
learnings



Observation and recall of information
Knowledge of dates, events, places
Students extend and refine their
knowledge so that they can use it
automatically and routinely to
analyze and solve problems and
create solutions.
Student Thinking
Students Thinks and Works
(Relationships Important)
(Relationships Critical)
A
B
Acquisition
Application
Students gather and store bits of
knowledge and information and
are expected to remember or
understand this acquired
knowledge.
Students use acquired knowledge to
solve problems, design solutions,
and complete work. The highest
level of application is to apply
knowledge to new and unpredictable
situations.
3


Solve problems using
required skills and/or
knowledge
Make use of learning in new
or concrete manner, or to
solve problems
2



Order, group, infer causes
Interpret facts,
compare/contrast
Predict consequences
Remembering: “information
gathering”
Adaptation
Students have the competence that,
when confronted with perplexing
unknowns, they are able to use their
extensive knowledge base and skills
to create unique solutions and take
action that further develop their
skills.
Organize parts
Identify components
Separate into component
parts
Understanding: “confirming”


Assimilation
4
Applying: “making use of knowledge”

5
Verify value of evidence/
Recognize subjectivity
Make judgments/choices
based on criteria, standards,
and/or conditions
Analyzing: “taking apart”



C
Use innovation to make
something new
Generalize from given facts
Predict or draw conclusion


Mastery of subject matter
Gain specific facts, ideas,
vocabulary, etc.
Formula for Success:
Rigor x Relevance x Relationships = Meaningful Learning
(Note: if any one of these are missing, the equation equals
zero)
D
Studen
t
Driven
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Teacher Works
(Relationships of Little
Importance)
Classroo
m
Student Work
(Relationships Important)
RELEVANCE
R
I
G
O
R
Teache
r
Driven
Real
Life
Rigor and Relevance Model Adaptation
RELEVANCE
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C
D
R
I
A
B
G
O
R
RELEVANCE
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EKS:_____________________________
DOK: _________
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EKS:_____________________________
DOK: _________
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EKS:_____________________________
DOK: _________
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AUTHENTIC ASSESSMENT
According to the Virginia Department of Education, authentic assessment refers to
assessment by performance, task, product, or project. Authentic assessment asks
students to apply what they have learned in such a way that it provides evidence of indepth understanding, rather than of superficial or naive understanding. In authentic
assessment, teachers ask students to provide evidence that they have "gotten it" by
actually doing something real. Often, such assessments include an authentic
audience—real stakeholders to whom the students present information or with whom
they otherwise engage.
The DOE goes on to explain, “As students construct meaning from their inquiries, not
all students, no matter how hard teachers work with them, will arrive at the proper
scientific conceptions. The fact that some students have failed to grasp the principles
of scientific inquiry is often hidden when conventional, multiple-choice tests are used.
What this means for assessment and evaluation is that assessment must be processoriented. In assessing, teachers may want to consider questions such as the following:
 What are the contributions of the students?
 Are the claims viable in terms of the data collected (including
claims made by students who enter and pursue blind alleys in
their research)?
 How creative are the research questions?
 Are the findings consistent with currently held views?
 What skills did the students use, and how well were they used in
the process of finding answers to questions”
The design and content of an authentic assessment may depend upon how the
students' project has evolved. But in any case, if scientific inquiry is an important factor
in the project, the assessment should compel students to show clear evidence of
understanding the "big picture" of scientific inquiry (from organizing and supporting
questions, through research and data collection, to hypothesis testing and action).
Once the "big picture" or central learning of a unit has been identified, criteria for
judging student learning should be developed. Checklists are a useful way of
displaying criteria. Teachers can assign points to a checklist against a standard,
although assigning points is not necessarily straightforward. Students should have
access to the checklists as they perform. These tools can also make a judgment
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about the quality of their work, and this can be used as the basis for a discussion with
them about their progress throughout the project.
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